A primal-dual interior-point method based on a new kernel function with linear growth rate Y.Q. Bai † C. Roos † November 7, 2002 † Faculty of Information Technology and Systems Delft University of Technology P.O. Box 5031, 2600 GA Delft, The Netherlands e-mail: [Y.Bai,C.Roos]@its.tudelft.nl Abstract We introduce a new barrier function which has a linear growth term in its kernel function. So far all existing kernel functions have a quadratic (or higher degree) growth term. Despite this, a large-update primal-dual interior-point method based on this kernel function has the same iteration bound as the classical primal-dual method, which is based on the logarithmic barrier method. Keywords: Linear optimization, interior-point method, primal-dual method, complexity, kernel function. AMS Subject Classification: 90C05 1 Introduction We consider the linear optimization (LO) problems in standard format (P ) min{c T x : Ax = b,x ≥ 0}, where A ∈ R m×n (rank(A)= m), b ∈ R m ,c ∈ R n , and its dual problem (D) max{b T y : A T y + s = c,s ≥ 0}. We assume that both (P ) and (D) satisfy the interior-point condition (IPC), i.e., there exists (x 0 ,s 0 ,y 0 ) such that Ax 0 = b, x 0 > 0,A T y 0 + s 0 = c,s 0 > 0. It is well known that the IPC can be assumed without loss of generality. In fact we may, and will assume that x 0 = s 0 = e, where e denotes the all-one vector. For this and some other properties mentioned below, see, e.g., [7]. Finding an optimal solution of (P ) and (D) is equivalent to solving the following system. Ax = b, x ≥ 0, A T y + s = c, s ≥ 0, xs = 0, (1)